2 Answers
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Imagine your telescope optics looked like this red-hot glass!

Herschel's instruments look at the world in the wavelength range of 55–672 µm. When plotted as a function of wavelength, the thermal spectrum of a black body peaks$ \approx 5 k_\mathrm B T$. The boiling point of liquid helium is 4.2 K. The peak wavelength for something at that temperature would then be given by

$$\lambda_\mathrm{max} = \frac{h c}{5 k_\mathrm B T}.$$

With Boltzman constant$k_\mathrm B$ of about 1.381E-23 J/K and the Planck's constant of 6.626E-34 J s, the spectrum should peak at about 700 µm, so even if the optics were at liquid helium temperature it would be hard to see faint objects at longer wavelengths above the brightly glowing mirrors and optics.

The light reflected by the mirror was focused onto three instruments, whose detectors were kept at temperatures below 2 K (−271 °C). The instruments were cooled with over 2,300 litres (510 imp gal; 610 US gal) of liquid helium, boiling away in a near vacuum at a temperature of approximately 1.4 K (−272 °C). The supply of helium on board the spacecraft was a fundamental limit to the operational lifetime of the space observatory; it was originally expected to be operational for at least three years.

So they let the helium boil at very low pressure in order to bring its boiling point down to 1.4 K.

The main mirror was highly reflective in the infrared, which means its emissivity was low, probably down near 0.01. This helps reduce the emission even farther. According to the BBC's Herschel space telescope finishes mission the primary mirror was at about 90 K

For at least one of the instruments SPIRE internal mirrors and the sensors needed to be kept at 0.3 K. The refrigerator for that needed a cooling mass on its "hot side" and a slow boil-off of liquid helium provided such a sink.

The Herschel telescope had to be kept extremely cold to study its frigid targets

Okay Cold, but Why Helium and not the Cold of Space?

Cooling to space is limited by the Cosmic microwave background, and its characteristic temperature is about 2.7 K. That's just not cold enough for the telescope's optics.

Also, while radiating into the cold of space theoretically provides a source for cooling besides liquid helium, this is pretty inefficient and all it takes is a short exposure to the hot Earth or a tiny bit of Sunlight to warm everything up dramatically, rendering Herschel at least temporarily blind.

Instead, with the current design, the cold optical system can be boxed in and carefully insulated, and the boil-off of the Helium vented to space carries the heat away.

Herschel pictured the "cold cosmos" - places where gas and dust are coming together to form stars. Here, in the Rosette Nebula, in the constellation of Monoceros, a mass of new stars (bright spots) are just firing into life

$\begingroup$as far as I can tell helium refrigerants get down to 10-15K, well shy of that 3K target so glad I didn't post mine. Used to terrestrial IR Imagers that are working down near Nitrogen boiling point, not absolute zero so made some wrong assumptions.$\endgroup$
– GremlinWrangerJun 4 at 12:41

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$\begingroup$@GremlinWranger Yes, closed-cycle helium cooling can get down to near the boiling point, as you say. Open cycle systems can get to 0.3K (as in Herschel), but to go lower (or remain closed-cycle) the best terrestrial system we have is the dilution refrigerator, but this critically requires gravity to provide the separation force for the He3/He4 isotopes. Closed-cycle dilution refrigerators for space applications are currently in development, but were not a practical option, presumably, when Herschel was being designed.$\endgroup$
– J...Jun 4 at 16:57

$\begingroup$@J... He dilution refrigerators don't need gravity. They flew on the closely related Planck mission (same launch, same bus). One of the "highlights" of that mission was a critical shortage of He-3 right before launch.$\endgroup$
– user71659Jun 4 at 23:38

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$\begingroup$@user71659 Traditionally, they do if you close-cycle them, and due to the extreme cost of He-3, in terrestrial applications, they're usually run this way. The Planck cooler ran open-cycle (no gravity), which means it lasted about 30 months with the helium supply on board. That helium-3 was sacrificed to the void of space. Herschel didn't need sub-0.3K temperatures so other open-cycle methods were used that didn't need the very expensive He-3. New designs for closed-cycle He-3/4 separation exist which do not require gravity (capillary separation) but have not yet gone to space, afaik.$\endgroup$
– J...Jun 4 at 23:50

$\begingroup$If you exclude the requirement for liquid He, cooling is used more broadly, Above the entry level, even consumer astrocams are normally equipped with a thermo-electric cooler that lets them operate several dozen degrees below ambient to reduce noise.$\endgroup$
– Dan NeelyJun 4 at 16:05